Rays of light from Sun falls on a bi-convex lens of focal length and the circular image of Sun of radius is formed on the focal plane of the lens. Then [2007]

Question

Rays of light from Sun falls on a bi-convex lens of focal length $f$ and the circular image of Sun of radius $r$ is formed on the focal plane of the lens. Then [2007]

Smart Achievers · Accepted Answer

(2)

From the figure, in $r$ , $\tan β = \frac{A B}{A C}$

$\Rightarrow A B = A C \tan β$

$\Rightarrow 2 r = f \tan β$ $∴$ $r = \frac{f}{2} \tan β$

Hence, the area of the image formed by the Sun is

$π r^{2} = π \frac{\tan^{2} β}{2} f^{2} \propto f^{2}$

Solution

Q.
Rays of light from Sun falls on a bi-convex lens of focal length $f$ and the circular image of Sun of radius $r$ is formed on the focal plane of the lens. Then [2007]

1 Area of image is $π r^{2}$ and area is directly proportional to $f$

2 Area of image is $π r^{2}$ and area is directly proportional to $f^{2}$

3 Intensity of image increases if $f$ is increased

4 If lower half of the lens is covered with black paper area will become half

Ans.
(2)

From the figure, in $∆ A B C$ , $\tan β = \frac{A B}{A C}$

$\Rightarrow A B = A C \tan β$

$\Rightarrow 2 r = f \tan β$ $∴$ $r = \frac{f}{2} \tan β$

Hence, the area of the image formed by the Sun is

$π r^{2} = π \frac{\tan^{2} β}{2} f^{2} \propto f^{2}$

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Solution

Q. Rays of light from Sun falls on a bi-convex lens of focal length f and the circular image of Sun of radius r is formed on the focal plane of the lens. Then [2007]

1 Area of image is πr2 and area is directly proportional to f

2 Area of image is πr2 and area is directly proportional to f2

3 Intensity of image increases if f is increased